00:01
On this problem, this is essentially a conditional probability.
00:03
You know what the probability that a student with an a on the midterm will obtain a final grade of an a.
00:09
Now, essentially what is asking for is the probability of the final grade being an a, given that the midterm grade was an a.
00:20
So using our rules for conditional probability, this is equal to the probability of final and midterm over the probability of midterm.
00:32
So now we need to find these two parts.
00:35
So let's start with the finding probability of the final and the midterm.
00:43
We're told that the professor gives a final grade of an a to 20 % of the students, and of those 70 % obtained an a on the midterm.
00:52
So this would be 0 .20, that was for the final, times 0 .70.
00:58
That's the number of those that are down an a on the midterm.
01:03
Multiply these together gives us 0 .14.
01:06
And so that's the probability of final and midterm.
01:08
That would be 0 .14...